软正合序列的若干性质  

Properties of Soft Exact Sequences

作　　者：吴越 马晶[1] WU Yue;MA Jing(College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林大学数学学院

出　　处：《吉林大学学报（理学版）》2019年第6期1287-1291,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11771252;11771176)

摘　　要：利用模论和软模的基本性质讨论软同态的分解性质.首先,定义单的软模同态和软模序列的正合;其次,证明软同态都可以分解为一个满的软同态和一个单的软同态的复合;最后讨论软正合序列的基本性质,给出几类简单的软模序列正合的等价条件,并利用两个软正合序列构造一个新的软正合序列.By using module theory and the basic properties of soft modules,we discussed the decomposition properties of soft homomorphism.Firstly,we defined a single soft homomorphism of soft modules and soft exact sequence.Secondly,we proved that every soft homomorphism could be decomposed into the composition of an epimorphism and a monomorphism.Finally,we discussed the basic properties of soft exact sequences,and gave equivalent conditions for several kinds of simple soft modulus sequence to be exact,and constructed a new soft exact sequence by using two soft exact sequences.

关 键 词：软模 软同态 软正合序列 

分 类 号：O153.3[理学—数学]